Spheroidal multipolar expansions for intermolecular energy in crystal theory. Lattice energy and cell dimensions of the orthorhombic structure of benzene crystal

The oblate spheroidal formalism for the interaction energy between two non-overlapping ellipsoidal charge distributions is applied to the determination of the lattice energy and cell dimensions of the orthorhombic structure of benzene crystal. The molecules are assimilated to quadrupolar oblate ellipsoids and the pair potential is assumed to be a sum of two terms: a Kihara core-potential extended to oblate ellipsoids and the spheroidal quadrupolar interaction. The value so obtained for the lattice energy is -51.3 kJ mole^-1 at unit cell dimensions of 7.7, 8.1 and 7.4 A, while the observed heat of sublimation corrected for zero-point vibration is -52.3 kJ mole^-1 and the experimental cell dimensions are 7.39, 9.42 and 6.81 A at 138 K.     

Optical properties of a polydiacetylene crystal: poly-[1,6-di(N-carbazolyl)-2,4-hexadiyne]

Normal incidence reflection spectra and Kramers-Kronig transforms are reported for a polydiacetylene crystal, DCHD (substituent group: N-carbazolymethyl). The lowest energy optical transition for the polymer backbone is found at 15 300 cm^?1, the lowest value obtained thus far for a polydiacetylene. The polymer chain and the carbazolyl substituent group may be treated as isolated chromophores - the former dominating the visible portion of the spectra and the latter dominating the UV portion. Polarization studies for the (001) and (10$\text{1}\text{?}$) faces of DCHD permit unambiguous assignment of the two lowest energy transitions in the carbazolyl group at 28 750 cm^?1 and 33 250 cm^?1 as short- and long-axis polarized, respectively.     

Enthalpy of solvation, ΔHsolv0(CrO42−) (g), of gaseous chromate ion as estimated from lattice energy calculations

The enthalpy of solvation of the gaseous chromate ion, ΔH_solv⁰(CrO₄^2?) (g) is estimated on the basis of recent lattice energy studies made in this laboratory, and a charge distribution assigned to the ion. On the basis of the assigned charge of ?0.57 proton units to the oxygen atoms of the CrO₄^2? unit, the total lattice potential energies are found to be: U_pot(Na₂CrO₄) = 1836 kJ mol^?1; U_pot(K₂CrO₄) = 1717 kJ mol^?1; U_pot(Rb₂CrO₄) = 1645 kJ mol^?1 and U_pot(Cs₂CrO₄) = 1598 kJ mol^?1. The corresponding value for ΔH_solv⁰(CrO₄^2?) (g) = ?1077 kJ mol^?1.     

Role of CA2+ ion in the abortifacient action of prostaglandins. II. Molecular orbital and conformation energy calculations of PGA1

This paper reports some theoretical studies of PGA₁ using conformational and molecular orbital techniques. The conformation energy (CE ) calculations, using empirical potential-energy functions, for intrinsic torsional rotations around C₁₂? C₁₃ (θ), C₇? C₈ (Ψ), and C₁₄? C₁₅ (?) show a number of energy minima. The relative value of the CE for these minima ranges from 4.09 to 8.01 kcal/mol. An additional rotation around C₄? C₅ (χ) giving “twist” to the carboxyl chains lowers the CE value by 2–3 kcal/mol and a conformation with CE value 2.39 kcal/mol less than crystallographic one is obtained. The interchain interaction energy showed changes with conformations. No significant change in the interchain interaction energy was observed due to “twist” in the carboxyl chain. The isopotential mapping study demonstrated the probable ionic binding site near the carboxyl and the ring (O₉) oxygens. Conformational and molecular orbital results are discussed in the light of the reduced abortifacient potency of PGA₁ with respect to PGF_2α and the possible role of Ca²⁺ ions in this action.     

Thermoanalytical and spectroscopic studies on different crystal forms of nevirapine

This study is aimed at exploring the utility of thermoanalytical methods in the characterization of various polymorphs and solvates of nevirapine. The different forms obtained by recrystallization of nevirapine from various solvents showed morphological differences in SEM. The presence of polymorphic forms is suggested by single sharp melting endotherm different from original sample in DSC and no mass loss in TG, while appearance of desolvation peak in TG indicated the formation of solvates. The higher desolvation temperatures of all the solvates than their respective boiling point indicate tighter binding of solvent. The changes in the crystal lattice were demonstrated by X-ray powder diffraction studies. The enthalpy of fusion rule indicated the existence of monotropy in polymorphic pairs I/O and II/O, while I/II is enantiotropically related. The enthalpy of solution, an indirect measure of the lattice energy of a solid, was well correlated with the crystallinity of all the solid forms obtained. The magnitude of ΔH _sol was found to be ?14.26  kJ mol^?1 for Form V and ?8.29  kJ mol^?1 for Form O, exhibiting maximum ease of molecular release from the lattice in Form V. The transition temperature was found to be higher than the melting of both the forms except for polymorphic pair I/II providing complementary evidence for the existence of monotropy as well as enantiotropy in these polymorphic pairs.     

Kinetics of the thermal unimolecular decomposition of hex-1-ene-3-yne. Heat of formation and resonance stabilization energy of the 3-ethenylpropargyl radical

The thermal unimolecular decomposition of hex-1-ene-3-yne (HEY) has been investigated over the temperature range 949–1230 K using the technique of very low-pressure pyrolysis (VLPP). One reaction pathway is the expected C₅? C₆ bond fission to form the resonance-stabilized 3-ethenylpropargyl radical. There is a concurrent process producing molecular hydrogen which probably occurs via the intermediate formation of hexatrienes and cyclohexa-1,3-diene. RRKM calculations yield the extrapolated high-pressure rate parameters at 1100 K given by the expressions 10^16.0±0.3 exp(?300.4 ± 12.6 kJ mol^?1/RT) s^?1 for bond fission and 10^13.2+0.4 exp(?247.7 ± 8.4 kJ mol^?1/RT) for the overall formation of hydrogen. The A factors were assigned from the results of previous studies of related alkynes, alkenes, and alkadienes. The activation energy for the bond fission reaction leads to ΔH [H₂CCHCC?H₂] = 391.9, DH [H₂CCHCCCH₂? H] = 363.3, and a resonance stabilization energy of 56.9 ± 14.0 kJ mol^?1 for the 3-ethenylpropargyl radical, based on a value of 420.2 kJ mol^?1 for the primary C? H bond dissociation energy in alkanes. Comparison with the revised value of 46.6 kJ mol^?1 for the resonance energy of the unsubstituted propargyl radical indicates that the ethenyl substituent (CH₂?CH) on the terminal carbon atom has only a small effect on the propargyl resonance energy. © John Wiley & Sons, Inc.     

17O-RMN. d'éthers,de cétones et d'esters cycliques. Détermination de constante de couplage quadrupolaire

¹³C- and ¹⁷O-relaxation times measured in cyclic ethers, cyclic ketones, and lactones allowed the determination of the quadrupolar interaction at the O-site. Values obtained for six-membered rings can be used as standard values for ethers (χ = 13 MHz), ketones (χ = 10.5 MHz), and esters (χ = 11.5 MHz for dicoordinated and 9.5 MHz for monocoordinated O-atom). Even within a series, no correlation is found between the ¹⁷O-chemical shift and the value of quadrupolar interaction.     

Polar anchoring strengths of nematic liquid crystal on high-density polymer brush surfaces

ABSTRACT

Herein, the polar anchoring energy coefficient (A_θ) of nematic liquid crystal (NLC) was examined for high-density polymer brushes via capacitance measurements. The A_θ is 10^?4 J m^?2 for the brushes of poly(methyl methacrylate), poly(ethyl methacrylate) and poly(styrene). The value decreases to 10^?5 J m^?2 for poly(n-butyl methacrylate) and poly(hexyl methacrylate) with lower glass transition temperatures. However, each polymer brush displays a constant A_θ value over a temperature range of ?15°C to 90°C, which is hardly affected by the graft density and brush thickness. At 25°C, A_θ is 10 times greater than the corresponding azimuthal anchoring energy coefficient (A_φ); therefore, NLCs on polymer brushes can be preferentially aligned along the in-plane component of the applied field.     

The geometric and electronic structures of I3− and I5− from effective-potential calculations

The (ab initio) effective-potential theory developed by Ewig et al. is applied to the structures of the polyiodide ions, I₃^? and I₅^?. The bare ions I₃^? and I₅^? are found by optimization of the geometry to be symmetric and linear. The counterion environment, however, greatly influences the equilibrium structure. A symmetric, flexible counterion environment produces only a slightly altered symmetric, linear equilibrium structure for the I₃^? anion ; whereas an asymmetric, rigid counterion frame leads to unequal bond lengths and bending of the anion. For the I₅^? anion, the potential energy calculated for bending of the central I—I—I angle, α, is very small so that a slight interaction with the lattice will readily lead to the experimental bent structure with α = 94°. At this value of α, the two outer angles are found to be equal and close to the experimental value. The electronic structures of the I₃^? and I₅^? ions are also discussed.     

Ab initio determination of the ground-state potential energy curve for Ar2

A totally ab initio potential energy curve for Ar₂ is constructed by adding individually damped dispersion terms to an accurate single configuration self-consistent-field repulsive interaction curve. However, the well depth (77 cm^?1) of our computed curve is significantly less than the experimentaly deduced value (99.4 cm^?1)     

Hydrogen bonds and local symmetry in the crystal structure of gibbsite

First‐principles quantum mechanical calculations of NMR chemical shifts and quadrupolar parameters have been carried out to assign the ²⁷Al MAS NMR resonances in gibbsite. The ²⁷Al NMR spectrum shows two signals for octahedral aluminum revealing two aluminum sites coordinated by six hydroxyl groups each, although the crystallographic positions of the two Al sites show little difference. The presence of two distinguished ²⁷Al NMR resonances characterized by rather similar chemical shifts but quadrupolar coupling constants differing by roughly a factor of two is explained by different character of the hydrogen bonds, in which the hydroxyls forming the corresponding octahedron around each aluminum site, are involved. The Al‐I site characterized by a C_Q = 4.6 MHz is surrounded by OH? groups participating in four intralayer and two interlayer hydrogen bonds, while the Al‐II site with the smaller quadrupolar constant (2.2 MHz) is coordinated by hydroxides, of which two point toward the intralayer cavities and four OH‐bonds are aligned toward the interlayer gallery. In high‐resolution solid‐state ¹H CRAMPS (combination of rotation and multiple‐pulse spectroscopy) four signals with an intensity ratio of 1:2:2:1 are resolved which allow to distinguish six nonequivalent hydrogen sites reported in the gibbsite crystal structure and to ascribe them to two types of structural OH groups associated with intralayer and interlayer hydrogen bonds. This study can be applied to characterize the gibbsite‐like layer—intergallery interactions associated with hydrogen bonding in the more complex systems, such as synthetic aluminum layered double hydroxides. Copyright © 2010 John Wiley & Sons, Ltd.     

A program for calculation of crystal conformations of flexible molecules using convergence acceleration

Formulas are given for convergence-accelerated lattice sums over all intermolecular Coulomb, London, and repulsive interactions. Their implementation in the consistent force field is described. Optimum values of convergence constant and summation limit are found for r^?12, r^?9, and r^?1 interaction terms. Energy minimization in all degrees of freedom, also intramolecular, for crystals of Ar, KCl, and C₂H₆ is reported.     

Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates

The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. The described algorithm exploits the properties of the prolate spheroidal coordinates. The overlap and the kinetic integrals in ?³ are reduced to the integrals over the rectangular domain in ?², what substantially reduces the complexity of the problem. We prove that the integrand over the rectangular domain is continuous and does not have any slope singularities. For calculation of the integral over the rectangle any adaptive algorithm can be applied. The exemplary results were obtained by application of the adaptive Gauss quadrature. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A theoretical study on the effect of intercalating sulfur atom and doping boron atom on the adsorption of hydrogen molecule on (10,0) single-walled carbon nanotubes

Adsorption of molecular hydrogen on single-walled carbon nanotube (SWCNT), sulfur-intercalated SWCNT (S-SWCNT), and boron-doped SWCNT (BSWCNT), have been studied by means of density functional theory (DFT). Two methods KMLYP and local density approximation (LDA) were used to calculate the binding energies. The most stable configuration of H₂ on the surface of pristine SWCNT was found to be on the top of a hexagonal at a distance of 3.54 Å in good agreement with the value of 3.44 Å reported by Han and Lee (Carbon, 2004, 42, 2169). KMLYP binding energies for the most stable configurations in cases of pristine SWCNT, S-SWCNT, and BSWCNT were found to be ?2.2 kJ mol^?1, ?3.5 kJ mol^?1, and ?3.5 kJ mol^?1, respectively, while LDA binding energies were found to be ?8.8 kJ mol^?1, ?9.7 kJ mol^?1, and ?4.1 kJ mol^?1, respectively. Increasing the polarizability of hydrogen molecule due to the presence of sulfur in sulfur intercalated SWCNT caused changes in the character of its bonding to sulfur atom and affected the binding energy. In H₂-BSWCNT system, stronger charge transfer caused stronger interaction between H₂ and BSWCNT to result a higher binding energy relative to the binding energy for H₂-SWCNT.     

Synthesis and crystal structure of aquachlorobis(1,10-phenanthroline)manganese(II) nitrobenzoate trihydrate

The title compound has been prepared and its crystal structure determined by X-ray diffraction methods. The complex salt consists of Mn(II) complex cations, benzoate anions and lattice water molecules. Mn(II) assumes a distorted octahedral geometry defined by two 1,10-phenanthroline (phen) ligands, a Cl^? ion and a water molecule. A comparison of bond distances and bond angles suggests electrostatic interaction between Mn(II) and coordinated N atoms. The nitrobenzoate anion does not coordinate to the Mn atom but links with the complex cation via O?H···O hydrogen bonds. Aromatic stacking occurs between phen rings and between phen and benzoate.     

Syntheses,crystal structures,and magnetic properties of 1-D coordination polymers

Three coordination polymers of Robson-type macrocycles, {[Cu₄L¹(4,4′-bipy)₂]·4ClO₄·H₂O}_∞ (1), {[Cu₄L²(4,4′-bipy)₄]·2CH₃CN·4ClO₄·2H₂O}_∞ (2), and {[Zn₂L²(4,4′-bipy)₂]·(ClO₄)₂}_∞ (3) (where H₂L¹ and H₂L² are the [2?+?2] condensation products of 1,3-diaminopropane with 2,6-diformyl-4-methylphenol and 2,6-diformyl-4-fluorophenol, respectively), have been synthesized and characterized. Magnetic susceptibility was measured for 1 and 2 from 2 to 300?K. The optimized magnetic data were J?=?–368.5?cm^?1, J′?=?40.5?cm^?1 with R?=?1.69?×?10^?6 for 1 and J?=?–291.22?cm^?1, J′?=?83.74?cm^?1, ρ = 0.00168 with R?=?1.8?×?10^?11 for 2, respectively. The data reveal strong antiferromagnetic interactions between two Cu(II) ions in the macrocyclic unit and ferromagnetic interaction between the Cu(II) ions in two adjacent macrocyclic units for 1 and 2.     

Analytical determination of anchoring energy coefficient in liquid crystal cells

An analytical solution for the anchoring energy coefficient of liquid crystal (LC) cells with arbitrary values of pretilt angles is derived. When phase retardation is plotted against applied voltage, one acquires the extrapolation length of the anchoring, and the anchoring energy coefficient is derived in the low-voltage regime. This solution can be applied to LC cells with various pretilt angles straightforwardly. Finally, the anchoring energy coefficient of 4.9 × 10^?5 J/m² is obtained for a homemade LC cell with a pretilt angle of 32.7°.     

Collisional energy transfer to methane by octupole coupliing

A linear molecule or one electron atom interacting with a tetrahedral molecule is considered. Formulae are presented for various rotationally averaged E → R and V → R first order transition probabilities arising from dipole-octupole (R^?5) and quadrupole-octupole (R^?6) coupling. Relatively large amounts of rotational energy can be transferred in first order (ΔJ ? 3). With CH₄ as the octupolar partner, energy transfer upto 350 cm^?1 at room temperature is shown to proceed very efficiently. For the 5²P_{$\text{3}\text{2}$} → 5²P_{$\text{1}\text{2}$} transition in Rb, σ_qu is calculated to be ? 28 A² in quite good agreement with experiment and using an independent value of the octupole moment of CH₄. Energy transfer above 350 cm^?1 becomes rapidly less efficient. Among V → R transfer processes in the 500–700 cm^?1 range, the long range mechanism is almost certainly not the dominant one in the relaxation of CO₂⁺ (010) by CH₄ (σ_calc ≈ 10^?3 σ_obs) but will be important in the relaxation of SO₂.     

Polarization energy of a localized charge in a molecular crystal. VI. Effect of excitons

The polarization energy of a localized charge carrier in a molecular crystal changes by ΔP near an exciton, viewed as a localized excited molecule of changed polarizability. Experimental polarizability changes in the first excited singlet state are used to calculate ΔP for various carrier and exciton positions in benzene, naphthalene, anthracene and tetracene. As the excited-state polarizability is larger, ΔP is normally negative, with minima ranging from ?12 meV in benzene to ?83 meV in tetracene. The change in charge-quadrupole energy ΔW_Q is estimated for naphthalene using a theoretical quadrupole moment for the first triplet state. At most sites |ΔW_Q| > |ΔP|, but the sign of ΔW_Q varies. The net exciton interaction with electrons in naphthalene varies from ?49 to +45 meV and with holes from ?106 to +29 meV. This behaviour is broadly complementary to that previously calculated for vacancies.